Note that 1. Eachvalvethusconductsforaperiodof1200,whenitis conducting. 2. The magnitude of valve current is Id, the valves in the upper rowcarrypositivecurrentandthevalveinthelowerrow carry negative current.3. The current in each phase of the ac source is composed of currentinthetwovalvesconnectedtothatphase.For example ir= i1i2(i.e., the current in the secondary winding of the transformer. 4. Thetransferofcurrentfromonevalvetoanothervalveinthesamerowiscalledcommutation.Inthisanalysis source inductance has been assumed to be negligible. Therefore commutation occurs instantly i.e., without overlap. 5. The grid or gate control can be used to delay the ignition of the valves. The delay angle delay angle is denoted by and it corresponds to time delay of /.6. Withdelayangle valve3ignitesatt= insteadoft=0.similarlyvalve-4atat t=600+ valve-5atatt=1200+.7. The ignition may be delayed upto t=1800for phase y. beyond this eyis no longer greater than er. hence valve-3 will not ignite.Average direct voltage or DC voltage :rbe, 0 t to 60 t From0 0= = is available at output. In this case valve-1 and valve-2 conduct and each valveconductsfrom t=600+ to t= (i.e., total angle of 600)( ) ( )0 0180 60 + = = t cos E t cos E e e em m b r rb ( ) ( )0 0 0m m2E sin t 60 sin120 3E sin t 60 = = ( )0 0m3E cos 90 60 t = + ( )030 3 + = t cos Em( )0m3E sin60 t = ( ) t d e26V060rb d= + ( ) ( ) t d 30 t cos E 3260600m+ = + ( ) + = d 30 cos E 3260600m[Assuming] = t( )00m603 3Esin 30 = +( ) ( ) [ ]0 0030 30 + = sin sin Vd[Here mdEV3 30=] cos sin Vd0030 2 = cos V Vd d 0= Now, = ==phphm0 dE 6 3E 23 3 E 3 3V=phERms value of phase voltage Again, L LphdE EEV2 336 36 30= = ==LERms value of line voltage Note thatIf I be a non-sinusoidal time varying current, then it may be resolve into a number of sinusoidal and co-sinusoidal components containing fundamental and higher order harmonics. where, ( ) cos I A of Average 21 =and ( ) sin I B of Average 21 =Concept of harmonic analysisFundamental component of I = 11 1 2121 1ABtan B A I + =The fundamental component may be calculated as follows:Output current: The voltage and current waveform for phase R is shown below:Let us assume,t cos E em r =and here, dI I=Therefore, ( ) cos I A of Average 21 = d cos Id=00606020060d602I sin=d dI3 2232 I2= =and ( ) sin I B of Average 21 = 02006060== d sin Id011 1 2121 103 2 = + = dIABtan B A Id rmsI I 621 3 21= = = rms value of fundamental component of current in phase R.d2 3 3I2 2 | | = | ` \ )Let us consider only fundamental component of current in phase Rd rms rmsI I I61= = = rms value of transformer secondary current.If losses in the converter be neglected, the AC power input must be equal to DC power output.DC ACP P = Or, cos I Erms ph3rmsphI cosE66 3 =and phd d rms3 6EV cos I I6 (= =( ( QOr, cos I Erms ph3 cos I Erms ph3 = cos cos = Load current,= =LdLRVI cosRELL2 3Ld03 2EV (= ( Q( ) R phase for0 0 At sin I E sin I E Q , P P ,R R rms ph max= = = = =AC DC ph rms ph rmsP P 3E I cos 3E I cos = = =AC ph rms ph rmsQ 3E I sin 3E I sin = =maxQ Q , P , = = = 0 90 At0Therefore we see the converter whether is acting as rectifier or as an inverter, draws reactive power from ac system.Different types of HVDC links used in HVDC transmission:A. MONOPOLAR LINKS:1. It uses one conductor, usually of negative polarity. The return path is ground or water (sea).2. Instead of ground return a metallic return may be used in situations where earth resistivity is too high or possible interference with underground or underwater metallic structure is objectionable.0 Q , P P , 180 Atmax0= = = If Negative 900= P , Converter will act as an inverter.B. BIPOLAR LINKS:1. It has two conductors, one positive and the other negative.2. Each terminal has two converters of equal rated voltage, connected in series on the DC side. The junction between the converters is grounded.3. Normally the currents in the two poles are equal and there is no ground current.4. Thetwopolescanoperateindependently.Ifonepoleisisolated duetofaultonitsconductor,theotherpolecan operate with ground and thus carry half the rated load or more by using overload capabilities of its converter and line.5. From the view point of lighting performance, a bipolar HVDC line is considered to be effectively equivalent to double circuit AC transmission line. 6. Undernormaloperationitwillcauseconsiderablylessharmonicinterferenceonnearbyfacilitiesthan MONOPOLAR links.7. whengroundreturnisnotpossible(duetohighearthresistivity),metallicreturnisused.Itservesasthereturn path when one pole is out of service or when there is imbalance during bipolar operation. 8. Thethirdconductorrequireslowinsulationandmayalsoserveasashieldwireforoverheadlines.Ifitisfully insulated, it can serve as a spare.C. HOMOPOLAR LINKS:1. Two or more conductors have same polarity, usually negative polarity because it causes less radio interference due to corona.2. Thereturnpathisground.Whenthereisafaultinoneconductorentireconvertersisavailableforfeedingthe remaining conductors which having some overload capability can carry more than normal power.3. In the contrast, for BIPOLAR SCHEME reconnection of the whole conductor in one pole is more complicated and usuallynotfeasible.HOMOPOLARconfigurationoffersadvantageinthisregardinsituationswherecontinuous ground current is acceptable.4. The ground current may have side effects on gas or pipeline that lies within a few miles of the system electrodes. Pipelinesactsasconductors forgroundcurrentwhichcancausecorrosionofmetal.Thereforeconfigurationwith ground return may not be possible.Each of these HVDC system configurations usually has1. Cascaded group of several converters each having transformer bank and group of valves.2. The converters are connected in parallel on AC side and in series on DC side to give desired voltage level from pole to ground.Following are the types of application for which HVDC transmission line has been used:1. ACtransmissionisimpracticalforunderwatercablelongerthan30KMduetohighcapacitancerequiring intermediate compensation station.2. Asynchronous link between two AC system where AC ties is not feasible because of system stability problem or a difference in nominal frequency of the two systems.3. Forlargeamountofpowertransmissionoverlongdistancesbyoverheadline,HVDCisacompetitive alternative in excess of about 600KM.A bipolar scheme with all of its components is shown below:DC smoothening reactor (SR):1. Decreases harmonic voltage and current in the dc line.2. Prevents commutation failure in inverters3. Limits crest current in the rectifier during short circuit on dc line.4. Decreases the incidence of commutation failures in the inverter during dips in the alternating voltage.5. Smoothenstherippleinthedirectcurrentsufficientlytopreventthecurrentfrombecomingdiscontinuousat light loads.A dc reactor is connected in series with each pole of a converter station. Its inductance lies in range of 0.4 to 1H. The value of inductance of the reactor should be such that a resonance of the dc circuit does not occur at power frequency.It serves the following purposes:A simple HVDC transmission systemDC output of converter = cos V0 dIf > 900converter will act as inverter. Therefore HVDC terminals can be designed to operate both in rectifier and inverter mode by controlling delay angle .Actually, two HVDC converters are connected on both sides. Method of reversal of power flow:For forward power flow (from Stn-1 to Stn-2), is controlled between 00to 900at Stn-1 and between 900to 1800at Stn-2.The-control is just opposite for reversal of power flow.Advantages of HVDC transmission system1. No stability problem with Dc line, hence there is no longer length limitation with DC.2. There is no skin effect with DC, hence power loss are reached marginally. 3. A DC transmission line requires no reactive compensation.4. Power flow through DC tie lines can be controlled more rapidly and accurately. Disadvantages of HVDC transmission system1. Circuit breaking is difficult in DC circuit.2. DC system does not have transformer to change the voltage level.3. Cost of terminal station is very high.4. Both AC and DC harmonics are generated. AC and DC filiters are required to minimize harmonics involving high cost.HVDC Systems in IndiaHVDC has been incorporated in the Indian grid also. The following two systems have been commissioned in 1991.(a)Rihand-DelhiHVDCSystem: A 500kV,1500MW,810kmbipolarHVDCline hasbeensetupbetweenRihand andDelhitotransmitbulkpowerfromRihand/Singrauli complextoDelhi.Itisdesignedtooperateinthe following modes: bipolar, monopolar with ground return, monopolar with metallic return.(b) Vindhyachal HVDC back to back System: This back to back link is for exchange of power between Northern and Westernregions..Eachblockof250MWiscapableofoperatingindependentlyineitherdirectionandcantransfer power in the range of 25 MW to 250 MW depending on system conditions.Inadditiontoabove,Chandrapur backtobackproject (2x500MW),Chandrapur-Padghe bipolarsystem(500kV, 1500 MW, 736 km), Jeypore back to back project (2 x 250 MW) and Mau back to back project (2 x 250 MW) are also proposed.